Finite-size rescaling transformations

Abstract

A theory of finite-size rescaling transformations (FSRT) is derived. It yields accurate estimates of the critical properties of statistical-mechanical systems of infinite extent. The arguments used are analogous to, but different from, conventional renormalization-group theory. The FSRT do not involve block spins and do not introduce any new couplings beyond those already in the problem. A technique which was suggested phenomenologically by Nightingale is derived as a special case of the FSRT theory. The optimization of convergence rates, and the relationship between FSRT and the finite-size scaling hypotheses of Fisher, are examined. Some new numerical results are presented.